In radar and communication systems for various practical reasons such as peak power efficiency and system efficiency, a constant envelope signal in time domain is desired as the transmit signal. Usually the Fourier transform magnitude (frequency domain) of the transmit signal may be known because of optimization considerations involving the known target and interference spectral characteristics. In that case, the problem is to generate a constant envelope signal in the time domain as in FIG. 1B whose Fourier transform magnitude function matches with the prescribed Fourier transform magnitude in the frequency domain (FIG. 1A).
Previous methods to generate specific cases of this general problem—specifically a chirp-like signal with constant envelope that has a notched spectrum—is described in a patent by Ferrell and Woody [U.S. Pat. No. 5,852,418, Notched-Spectrum Swept-Frequency Generator and Method Therefore, U.S. patent Issued on Dec. 22, 1998], as well as in [M. J. Bennett, T. Anderson, and W. N. McDicken, “Frequency Notched Waveforms for Medical Ultrasound Imaging”, 2007 IEEE Ultrasonic Symposium, pp. 789-792, New York, N.Y., 28-31 Oct. 2007]. The methods described in those previous works mainly address generating a constant envelope signal with notched type of spectrum by exploring variations of the method for generating the standard chirp signal.